I always thought a quarter wave on two metres (145MHz) was about 19 inches. I've made 2m dipoles with 19in. elements and they seemed to work. I have one of those telescopic whips with a BNC connector to use with 2m handies, and the length when fully extended was 19in.
So I was a bit surprised when I plugged this telescopic into my FT-817 to note that it resulted in an SWR reading of three bars. After a bit of experimentation I croc-clipped a bit of stiff wire on to the end of the whip and found I could get the SWR down to no bars with a total length of about 22.5 inches. And not only did the SWR go down but the strength of a repeater I was monitoring came up.
I decided to look at the 19in whip using my AA-200 antenna analyzer. Sure enough, the dip in the SWR was some way to the right of 145MHz.
An antenna analyzer by itself doesn't provide much of a ground plane, so I attached a quarter wave counterpoise. This begged the question of what length to use. Since old habits die hard, I used 19 inches for this. There seemed to be some interaction between the length of the counterpoise and the SWR plot. Instead of a sharp null I got a broader valley with two dips. Nevertheless it still worked out that 22 or 23 inches gave a better match. Go figure!
I also thought that a 3/4 wave vertical will match to 50 ohms, so that a quarter wave on 2m will work on 70cm as well. Well, nobody has told my FT-817, which moans "HIGH SWR!" if I try to transmit on 70 into this 2m whip. My antenna analyzer doesn't go up above 200MHz, so I can't investigate this.